login
Number of polyhexes rooted at a hexagon and containing n hexagons.
(Formerly M3907 N1603)
2

%I M3907 N1603 #26 Oct 14 2023 23:49:42

%S 1,1,5,20,84,354,1540,6704,29610,131745,591049,2669346,12131148,

%T 55431285,254539897,1174027598,5436826110,25269402555,117838870833,

%U 551192276450,2585418254532,12158383558066,57313008207960

%N Number of polyhexes rooted at a hexagon and containing n hexagons.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A002213/b002213.txt">Table of n, a(n) for n = 1..200</a>

%H F. Harary and R. C. Read, <a href="https://doi.org/10.1017/S0013091500009135">The enumeration of tree-like polyhexes</a>, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.

%F G.f.: x + x*U(x) + (3/2)*x*U(x)^2 + (1/2)*x*U(x^2) + (1/3)*x*U(x)^3 + (2/3)*x*U(x^3), where U(x) = (1 - 3*x - sqrt((1-x)*(1-5*x)))/(2*x).

%F a(n) ~ 5^(n+1/2)/(2*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Aug 13 2013

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

%E Edited by _Emeric Deutsch_, Feb 18 2004